Rotational Nonequilibrium Research Articles

Rotational nonequilibrium in state-resolved models for shock-heated flows

The effects of molecular rotation on the dynamics of high-temperature nonequilibrium flows is investigated in this work, with an application to nitrogen shocked flows. The overall manifold of rovibrational levels for the ground electronic state of N2 is firstly obtained through the solution of the radial Schrödinger equation over a high-fidelity potential curve. The obtained solutions predict the existence of 9510 states, including quasi-bound states which may spontaneously dissociate through tunneling effects. The lifetimes of such quasi-bound states are determined using a semiclassical method, and most of them are found to be long-lived. A semi-empirical rate for state-specific rotational translations has then been applied so as to examine the importance of rotational dissociation against vibrational dissociation, in equilibrium conditions. Rotational dissociation is found to be one to two orders of magnitude below vibrational dissociation, from low temperatures up to 100,000K. The contribution of quasi-bound states to the overall dissociation rate is also found to be essentially negligible (increase of the rotational dissociation rate by a factor of 1.5–2 in the whole temperature range). Finally, as the full state-specific modeling of the interactions of this large number of rovibrational levels remains out of reach of the state of the art theories and computational resources, a simplified state-specific model for the simulation of shocked flows is proposed, treating vibration-translation and rotation-translation interactions in an uncoupled fashion. A Boltzmann equilibrium distribution is considered for each subset of rotational levels, for each of the molecular vibrational levels, at a characteristic rotational temperature Trotv. Rotational collisional numbers are calculated according to the method recently proposed by Park and confirm the rapid increase of the number of collisions needed for establishing rotational–translational equilibrium, as the gas temperature rises. The results of our simulations also confirm the claims by Park that for high temperatures (roughly above 12,000K), rotational–translational equilibration actually occurs after vibrational-translational equilibration, contrary to the popular belief.

Experimental Analyses of High Knudsen Number Flows

In late years, the necessity of high Knudsen number flows, such as highly rarefied gas flows with large mean free path and gaseous flows around nanodevices with small characteristic length have increased significantly, especially in fields of researches on space technology, surface science, fabrication of thin film for semi-conductor and so on. In this paper, we describe mainly the optical diagnostic techniques for the high Knudsen number flows, such as laser induced fluorescence (LIF), resonantly enhanced multiphoton ionization (REMPI) and pressure sensitive molecular film (PSMF), and our experimental results obtained by the use of the techniques, i.e., applications of LIF to visualization of flow field structures including complicated shock wave system and to a measurement of rotational temperature, establishment of a REMPI system and its application to detection of rotational nonequilibrium in highly rarefied gas flows, and development of the suitable PSMF for low density and micro-scale gas flows.

An axisymmetric computational model of generalized hydrodynamic theory for rarefied multi-species gas flows

On the basis of the Eu’s generalized hydrodynamic (GH) theories for diatomic single species gas and monatomic multi-species gas, an axisymmetric GH computational model for multi-species gas containing monatomic and diatomic molecules is developed for the numerical simulation of hypersonic rarefied gas flows. The multi-species GH computational model includes monatomic and diatomic species of O 2 , N 2 , NO, O, N. The mass diffusion flux of the gas mixture is included in the GH constitutive relation. In addition, the physical relationship between the mass diffusion and heat fluxes is added to the evolution equation set. The multi-species GH theory includes the rotational nonequilibrium effect of diatomic molecules by introducing excess normal stress associated with the bulk viscosity. An efficient multi-species GH numerical solver for axisymmetric rarefied flows is then developed by adopting various numerical techniques, such as an adequate nonlinear equation solver for the GH constitutive relation, an accurate flux splitting scheme, multi-grid convergence acceleration and slip-wall boundary conditions. For validation, the proposed computational model is applied to hypersonic rarefied flows over a space shuttle nose, a sphere and a reentry body as well as 1D shock structure. By comparing the results of the multi-species GH model with those of the Navier–Stokes equation and the DSMC, the accuracy and physical consistency of the GH computational model are critically examined.

A generalized Bhatnagar–Gross–Krook model for nonequilibrium flows

The Bhatnagar–Gross–Krook (BGK) model approximates the collision term of the Boltzmann equation by a single relaxation process from a nonequilibrium state to an equilibrium state. From the BGK model, the Navier–Stokes, Burnett, and Super-Burnett equations can be derived. However, the success of these derived macroscopic equations in the description of highly nonequilibrium flow is limited. In order to extend the validity of the BGK model to cope with complicated physical relaxation processes, we propose a generalized BGK (GBGK) model, where the gas distribution function settles to an equilibrium state through multiple particle collisional processes. The GBGK model can be used to capture the transitional, rotational, and vibrational nonequilibrium flow phenomena. More importantly, it may provide a theoretical framework to derive new macroscopic governing equations which are valid in the near continuum flow regime.

REMPIによる希薄気体流の回転モード内温度非平衡解析(J11-4 量子・分子熱流体工学(4),J11 量子・分子熱流体工学)

REMPIによる希薄気体流の回転モード内温度非平衡解析(J11-4 量子・分子熱流体工学(4),J11 量子・分子熱流体工学)

A generalized hydrodynamic computational model for rarefied and microscale diatomic gas flows

On the basis of Eu's generalized hydrodynamics, a computational model is developed for the numerical simulation of rarefied and microscale diatomic gas flows. The rotational nonequilibrium effect is taken into account by introducing excess normal stress associated with the bulk viscosity of the gas. The computational model for diatomic gases reduces to the model for monatomic gases in the limit of vanishing bulk viscosity. The thermodynamically consistent computational model is applied to the one-dimensional shock wave structure and the two-dimensional hypersonic rarefied flow around a blunt body in order to demonstrate its capability and validate the numerical results. The general properties of the constitutive equations are also presented through a simple analysis. The numerical results show that the new generalized hydrodynamic computational model yields the solutions in qualitative agreement with experimental data and DSMC results in the case of the problems studied.

On the presence of rotational nonequilibrium in a supersonic hydrogen-fluoride laser

Overtone small-signal gain data measured while operating a small-scale hydrogen-fluoride (HF) laser saturated on the fundamental transitions are compared with fundamental lasing output spectra and spontaneous overtone emission spectra measured orthogonal to the lasing axis. In all cases, the data are consistent with an equilibrium rotational distribution. These results are discussed in terms of their applicability to the question of rotational nonequilibrium in continuous wave HF lasers.

이원자 기체 일반유체역학 모델을 이용한 극초음속 희박 유동장 해석

희박상태나 극소장치에 관련된 기체운동을 해석하는 문제가 최근 중요한 연구주제로 부각되고 있다. 잘 알려진 DSMC와 더불어 모우멘트 기법, Chapman-Enskog 기법으로 분류되는 고차 비평형 유동 해석모델들이 이 문제에 적용되어 왔다. 본 연구에서는 Eu의 일반유체역학을 근간으로 이원자 기체에 관한 고차 해석모델을 개발하고자 한다. 회전 비평형 효과는 기체의 용적 점성계수에 관한 초과 수직응력을 고려하여 감안하였다. 개발된 계산모델을 일차원 충격파 내부구조와 단순 형상 외부의 희박 극초음속 유동장 해석에 적용하였다. 충격파 내부구조 및 전단유동 해석을 통해 회전 비평형에 의한 용적 점성계수 효과가 중요함을 확인하였다. 충격파 내부구조에 관한 이론적 예측이 실험과 잘 일치함도 확인하였다. The study of nonlinear gas transport in rarefied condition or associated with the microscale length of the geometry has emerged as an interesting topic in recent years. Along with the DSMC method, several fluid dynamic models that come under the general category of the moment method or the Chapman-Enskog method have been used for this type of problem. In the present study, on the basis of Eu's generalized hydrodynamics, computational models for diatomic gases are developed. The rotational nonequilibrium effect is included by introducing excess normal stress associated with the bulk viscosity of the gas. The new models are applied to study the one-dimensional shock structure and the multi-dimensional rarefied hypersonic flow about a blunt body. The results indicate that the bulk viscosity plays a considerable role in fundamental flow problems such as the shock structure and shear flow. An excellent agreement with experiment is observed for the inverse shock density thickness.

Experimental and numerical studies of rotational relaxation behind a strong shock wave in air

This paper describes the experimental and numerical investigations of unknown characteristics of the rotational nonequilibrium phenomena behind a strong shock wave in air. Experiments were carried out using a piston-driven shock tube with helium as driving gas and air as driven (test) gas, operated as a two-stage shock tube. In the experiments, emission spectra of NO were measured to evaluate the rotational temperature behind a strong shock wave. The numerical calculations use the computational code for the thermal and chemical nonequilibrium flow behind a strong shock wave developed by the present author's group, where 11 chemical species (N $_2$ , O $_2$ , NO, N, O, N $_2^+$ , O $_2^+$ , NO $^+$ , N $^+$ , O $^+$ , e $^-$ ) and 48 chemical reactions of high-temperature air are considered. The thermal nonequilibrium is expressed by introducing an 8 temperature model composed of translational temperature, rotational and vibrational temperatures for N $_2$ , O $_2$ , NO, and electron temperature. The coupling of a rotation, vibration and dissociation (CRVD) model was incorporated to take sufficiently into account the rotational nonequilibrium. The calculations were conducted for the same conditions as the experimental ones. From the calculated flow properties, emission spectra were re-constructed using the code for computing spectra of high temperature air “SPRADIAN”. Furthermore, rotational and vibrational temperatures of NO $\gamma$ (0,1) were determined from a curve fitting method and compared with the computed results.

Direct simulation Monte Carlo study of rotational nonequilibrium in shock wave and spherical expansion of nitrogen using classical trajectory calculations

The rotational nonequilibrium in a normal shock wave and in a steady spherical expansion is studied for nitrogen using the direct simulation Monte Carlo method coupled with classical trajectory calculations. The intermolecular potential for nitrogen is taken as an accurate potential energy surface constructed by van der Avoird et al. [J. Chem. Phys. 84, 1629 (1986)] and readjusted by Cappelletti et al. [Mol. Phys. 93, 485 (1998)]. The shock wave results are compared with the rotational distribution and the number density and rotational temperature profiles measured by Robben and Talbot [Phys. Fluids 9, 653 (1966)]. The agreement is generally good except at extremely low upstream temperatures, where the classical-mechanical treatment may be inadequate. The spherical expansion results are compared with the rotational distribution and the number density and rotational temperature profiles measured by Marrone [Phys. Fluids 10, 521 (1967)] and Coe et al. [Phys. Fluids 23, 706 (1980)] along the axis of a low density free jet expansion. It is shown that the rotational distribution gradually departs from a Boltzmann distribution farther downstream with an overpopulation in the higher rotational levels, in good agreement with the measured spectral data except near the orifice, where the spherical source expansion analogy may be inapplicable. The rotational temperature obtained by a Boltzmann fit at the low rotational levels or defined as the mean rotational energy agrees satisfactorily, except near the orifice, with the experimental rotational temperatures determined from the spectral data.

A Review of Recent Experiments and Calculations Relevant to the Kinetics of the HF Laser

A review of rate coefficients relevant to HF laser kinetics modeling is presented. The literature has been surveyed from the last published review in 1983 to the present. Updated HF Einstein emission coefficients are tabulated. Rate coefficients are categorized according to their role in the HF laser model: HF generation, reactive quenching, self-relaxation, V–V energy transfer, vibrational relaxation by atoms and molecules, F2 dissociation, and F atom recombination. In addition, a review of recent experiments and theoretical calculations relevant to the role of rotational nonequilibrium in HF lasers is presented. A list of recommended temperature dependent expressions for critical reaction rate coefficients is given.

K-1708 超希薄気体流中のREMPIによる回転温度非平衡解析(J08-2 熱流体現象の原子・分子論的アプローチ(2))(J08 熱流体現象の原子・分子論的アプローチ)

In this study, we develop the experimental system for 2R+2 N_2-REMPI and apply it to measure the rotational temperature in a supersonic free molecular nitrogen flow. There appear the non-equilibrium phenomena in the highly rarefied gas flows, such as the translational and rotational non-equilibrium and the rotational non-equilibrium. In this study, we find the strong rotational non-equilibrium in the free molecular nitrogen flow issued from the source chamber kept at 1.2 Torr into the expansion chamber at 3.2×10^<-5> Torr. The data in the Boltzmann plot, obtained from the REMPI spectra, can not be fitted by a line but approximately by two lines, revealing the non-Boltzmann distribution of the rotational energy in the ground state.

Fundamental gain suppression mechanisms in a continuous wave hydrogen fluoride overtone laser

When lasing occurs on the overtone, a rotational nonequilibrium computer model showed that the fundamental gains are determined by three independent mechanisms. First, overtone lasing decreases the gains of the P (7) and PiC/) lines whose upper or lower levels are directly involved in PioC/) overtone lasing. Second, overtone lasing reduces the rate at which the low/ v = 2 states are populated by rotational relaxation and increases the rate at which the low J v = 0 states are populated by rotational relaxation, resulting in suppression of the low J fundamental gains whose upper or lower levels are not directly involved in overtone lasing. Third, overtone lasing reduces the rate at which the HF(0, /) and HF(1, J) states are populated by the various collisional deactivation processes. The computer model gave reasonable agreement with the measured fundamental zero power gain profiles, Fabry-Perot power, and spectra. The model overpredicted the fundamental gain suppression (Aa) for the P (8,9) and P2(8,9) lines whose upper or lower levels were directly involved in overtone lasing and underpredicted the suppression for lines PI (4) and PI (4, 5). The model predicted the suppression for lines PI (5-7) and P2(6,7) reasonably well. When the rotational relaxation rate was increased by a factor of 10, the model was in reasonable agreement with the measured suppression, A a, of all P (4-9) and P2(4-9) lines. However, with the increased rotational relaxation rate, the model's prediction of the experimental zero power gain and residual fundamental gain profiles was not adequate. OMPARISON of residual fundamental amplification ratio (RF-AR) data obtained at relatively high medium saturation with two 99.7% reflective mirrors (asal = 0.00010015 and Ls = 30 cm) with the zero power amplification ratio (ZP-AR) data indicated that the gains of the low J lines P (4-6) and P2 (4-6) were suppressed between 41 and 96% and the gains of the high J lines PI (79) and P2(7-9) were suppressed between 3 and 44%.u The 1 -> 0 lines were suppressed more than the 2-> 1 lines. The maximum suppression occurred between 2 and 6 mm downstream from the nozzle exit plane, near the center of the 9-mm overtone beam. There was minimal suppression of lines P2 (8, 9). The low J fundamental gains were suppressed more than the high J fundamental gains even though their upper or lower levels were not directly involved in overtone lasing. Residual fundamental gain (RFG) measurements at low medium saturation with overtone mirrors of 99.7/98.0% reflectivity (asat = 0.000386787) showed weak suppression on lines ^i(7), P2(5), and PI (6) at axial positions between 2 and 6 mm downstream from the nozzle exit plane.' '2 There was no suppression measured for any of the other lines. RFG measurements performed at an increased level of medium saturation with 99.8/99.86% reflective overtone mirrors (asal — 0.000056716) resulted in essentially the same suppression obtained with the 99.7/99.7% mirrors.1-2 The objectives of this work were to determine why the low J fundamental gains were suppressed more than the high J fundamental gains even though their upper or lower levels were not directly involved in overtone lasing and to predict the RFG as a function of medium saturation. Since there are many kinetic processes involved in the population and depopulation of the upper and lower levels of the fundamental transitions, a detailed rotational nonequilibrium model (ORNECL)3'4 of the laser flow was used. When ORNECL was baselined to ZP-AR data, it was necessary to decrease the rotational relaxation (RR) rate5'6 by a factor of 10 and to include the multiquantum HF-H2 vibration-to-vibration (VV) transfer reactions.

Multilevel model of a pulsed chemical H2 — F2 laser and its promising operational modes

A pulsed H2—F2 laser has been investigated theoretically with the use of the authors' own multilevel laser model developed earlier. This model allows for the rotational nonequilibrium and anharmonicity of the HF molecules. The characteristics of a hydrogen fluoride laser have been calculated numerically for the conditions realised in various experiments. A comparison of the calculated and experimental laser parameters demonstrates that the proposed multilevel model describes well the operation of an H2—F2 laser. A numerical study is reported of promising, from the point of view of good energy and time characteristics, operational modes of a pulsed hydrogen fluoride laser at high (~5 bar) pressures in a mixture initiated by an electron beam and when the initiation is by flash photolysis of the active medium from an initial temperature of 100 K.

Monte Carlo computation of nonequilibrium flow in a hypersonic iodine wind tunnel

The nonequilibrium flow formed by the interaction of a freejet of iodine vapor impinging on a blunt body is investigated using numerical and experimental techniques. The computational approach employs the direct simulation Monte Carlo method. The experimental measurements consist of rotational temperature obtained along the flow axis and include portions of both the freejet expansion and blunt-body shock for four different stagnation conditions. Direct comparisons of the numerical results and the experimental data are quite successful at moderate temperatures. Hence, the rotational collision time of iodine is estimated in the temperature range of 100-500 K. At higher temperatures, the agreement between simulation and measurement is less satisfactory. This demonstrates the requirement for the development of a more detailed approach to simulating rotational nonequilibrium in high-temperature flows of diatomic species. 20 refs.

Theoretical simulation of lasers utilizing vibrational-rotational transitions in diatomic molecules allowing for anharmonicity and rotational nonequilibrium

A theoretical analysis of the operation of lasers utilizing vibrational-rotational transitions in diatomic anharmonic molecules was made taking into account the finite nature of the rotational relaxation rate. The conditions of validity of the equivalent two-level model describing these lasers were identified. Expressions for the populations of the upper and lower states participating in the lasing transition were derived using this model. Numerical calculations were made of the characteristics of an H2–F2 chemical laser using multilevel and two-level models and the results of the calculations were compared.

Analysis of rotational nonequilibrium in standing shock waves of nitrogen

The one-dimensional standing shock wave is the simplest flow in which nonequilibrium effects may be considered. The direct-simulation Monte Carlo method (DSMC) has yielded excellent agreement with results reported for the case of nitrogen flow at Mach 1.7. The DSMC technique is presently used in conjunction with a variable energy transfer probability model in which energy is transferred between the translational and rotational modes via the Borgnakke-Larsen (1975) phenomenological model.

Shape and width of IR absorption lines of ammonia expanded in a supersonic jet

Line-width and-shape of absorption lines of the ν2 vibration of ammonia were measured for a series of transitions starting from vibrational groundstate levels with a different rotational energy. An increase in linewidth was found for larger rotational energies of the initial states. This effect has been attributed to the spatial rotational non-equilibrium in the supersonic jet expansion.

Monte Carlo simulations in support of the Shuttle upper atmospheric mass spectrometer experiment

This paper presents the results of calculations obtained with a Direct Simulation Monte Carlo (DSMC) method that describes both the external flow about the nose region of the Shuttle Orbiter and the internal flow in an inlet tube that provides the initial path between the shock-processed gases and a mass spectrometer mounted inside the Orbiter. A dedicated, three-dimensional version of the DSMC was developed during this study for the internal flow simulation along with the procedure for interfacing the external and internal flows. The calculations span the 140 to 95 km altitude range, which includes most of the hypersonic transitional flow encountered during reentry. All calculations were for a multicomponent gas mixture consisting of five chemical species while simulating the effects of transitional, rotational, vibrational, and chemical nonequilibrium. The results of the calculations show that within the entry region of the inlet tube where the gas has equilibrated with the sidewall tube temperature, the pressure is substantially less than the pressure at the external surface. This pressure correction for the entry region is significant for all conditions investigated and increases with altitude. The results highlight the structure of both the external and internal flow. Results of parametric studies show the sensitivity of the equilibrated inlet sidewall pressure to mass flow rates, gas-surface reflection model, tube side-wall temperature variations, and surface recombinations.

Chemical laser grating selection measurements of initial vibrational energy distribution by reactions of F atoms with H2, CH4, C2H6

The complete product vibrational energy distribution from F+H2, CH4, C2H6 reactions was determined by the chemical laser grating selection (CLG) technique. Three important factors—vibrational relaxation and secondary reaction, rotational nonequilibrium, and superradiance were carefully investigated by time-resolved laser spectroscopy and analyzed by computer modeling. It was found that by using lower reactant pressure, these disadvantageous effects, which may have influenced the results of previous chemical laser studies, could be minimized or eliminated experimentally. It was also found that for these reactions, the accurate values of N2/N1 and N3/N2 could be obtained from the experiment or modeling calculation; in contrast, the value of N1/N0 was very high and was sensitive to vibrational relaxation and secondary reaction processes. In general, the results of the CLG method, at least for these reactions, are of the same degree of accuracy as those of the infrared chemiluminescence method. The rotational equilibrium assumption is still valid and can be used without apparent effect on the experimental results.